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arXiv · 2602.17576

Subluminal and superluminal velocities of free-space photons

Konstantin Y. Bliokh
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Abstract

We consider rectilinear free-space propagation of electromagnetic wavepackets using electromagnetic field theory, scalar wavepacket propagation, and quantum-mechanical formalism. We demonstrate that spatially localized wavepackets are inherently characterized by a subluminal group velocity and a superluminal phase velocity, whose product equals $c^2$. These velocities are also known as the 'energy' and 'momentum' velocities, introduced by K. Milton and J. Schwinger. We illustrate general conclusions by explicit calculations for Gaussian and higher-order beams and wavepackets, and also highlight subtleties of the quantum-mechanical description based on the 'photon wavefunction'.

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Konstantin Y. Bliokh. 2026-02-19. Subluminal and superluminal velocities of free-space photons. https://doi.org/10.1063/10.0044812

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